# Thermo-Electric toolbox

## 1. Notations

In the thermo-electric model, we have 4 parameters

• $\sigma$ the electrical conductivity

• $k$ the thermal conductivity

• $T_c$ the water cooling temperature

• $h$ the heat transfer coefficient

 These parameters can be scalars of fields.

We gather in the following table parameter ranges, nominal values as well as units for $\sigma, k, T_c, h$.

 Parameters Ranges Nominal value Units $\sigma$ $[52.10^{6};58.10^{6}$] $53\cdot 10^{6}$ $S \cdot m^{-1}$ $k$ $[360;380$] $370$ $W\cdot m^{-1} \cdot K^{-1}$ $T_c$ $[293;310$] $300$ K $h$ $[70000;90000$] $850000$ $W \cdot m^{-2} \cdot K^{-1}$

In the linear case, we first solve for $V$ and then for $T$ using $V$ to compute the Joule effect that generates heat inside $\Omega$.

## 2. Running the Thermo-electric application

Using Docker, you can run Feel++ model application and in particular the thermo-electric model using the following command

Docker command
``$docker run -it -v$HOME/feel:/feel feelpp/feelpp-toolboxes:latest``

Then type the following command in docker environment to run the model

Running Thermo-Electric model
``````$cd Testcases/models/thermoelectric/test$ mpirun -np 4 /usr/local/bin/feelpp_toolbox_thermoelectric_3d --config-file model.cfg``````